Eight queens puzzle

main.lua

--[[
 List all solutions that eight queens on the chess board can't attach each other
 
 example output:
  x - - - - - - - 
  - - - - x - - - 
  - - - - - - - x 
  - - - - - x - - 
  - - x - - - - - 
  - - - - - - x - 
  - x - - - - - - 
  - - - x - - - - 

]]--

-- size of the chess board
N = 8

function isPlaceOk(a, row, col)
  for i = 1, row - 1 do
    if a[i] == col or -- check any queen in the same column
      row - i == col - a[i] or --[[
        check any queen in the diagonal (top-left -> bottom-right)
        we use the slope value: k1 = (y2-y1) / (x2 - x1) where k1 = 1 to test the diagonal
        the other direction is k2 = -k1
      ]]--
      row - i == -1 * (col - a[i]) then -- check any queen in the diagonal (top-right -> bottom-left)
      return false
    end
  end
  return true
end

function draw(a) 
  for row = 1, N do
    for col = 1, N do
      io.write(a[row] == col and 'x' or '-', ' ')
    end
    io.write('\n')
  end
  io.write('\n')
end

--[[
  for each row, test each column and its following row (apply the same to the following row)
  until it completes all rows. 
]]--
function addQueen(a, row)
  if (row > N) then
    draw(a) -- draw the solution when it is complete.
  else    
    for col = 1, N do
      if isPlaceOk(a, row, col) then
        a[row] = col
        addQueen(a, row + 1)
      end
    end
  end
end

addQueen({}, 1)